Introduction to rational numbers quick check and practice and the answers
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Sure! Here is a brief introduction to rational numbers, followed by a quick practice and the answers:
Introduction to Rational Numbers:
Rational numbers are numbers that can be expressed as the ratio of two integers (where the denominator is not zero). They can be written in the form a/b, where a and b are integers and b is not zero. Rational numbers include fractions, decimals, and integers.
Quick Practice:
1. Which of the following numbers are rational?
a) 2/3
b) √2
c) -5
d) 0.75
2. Write the following decimal numbers as fractions:
a) 0.5
b) 0.8
c) -0.2
3. Simplify the rational expression: (6x^2 - 9xy + 3x) / (3x)
Answers:
1. a) 2/3 and c) -5 are rational numbers. b) √2 is an irrational number since it cannot be expressed as the ratio of two integers. d) 0.75 is a rational number because it can be expressed as 3/4.
2. a) 0.5 can be written as the fraction 1/2.
b) 0.8 can be written as the fraction 4/5.
c) -0.2 can be written as the fraction -1/5.
3. To simplify the rational expression (6x^2 - 9xy + 3x) / (3x), we can factor out the numerator: 3x(2x - 3y + 1) / (3x). We can cancel out the common factor of 3x from the numerator and denominator, leaving us with the simplified expression: 2x - 3y + 1.
Please note that the answers may vary depending on the context of the questions.
To introduce you to rational numbers, let's start with the definition. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers (whole numbers).
Now, for a quick check, I will provide you with a question that will test your understanding of rational numbers, and then I will guide you on how to solve it.
Question: Which of the following numbers is rational?
a) √3
b) -5
c) 0.7 (recurring decimal)
d) π (pi)
Answering this question will require identifying whether each number can be expressed as a fraction or ratio of two integers.
a) √3 - This is an irrational number because it cannot be expressed as a fraction of two integers.
b) -5 - This is a rational number as it can be expressed as the fraction -5/1.
c) 0.7 (recurring decimal) - This is also a rational number. Although it is a decimal, it can be converted to a fraction or ratio. In this case, 0.7 can be written as 7/10.
d) π (pi) - This is an irrational number as it cannot be expressed as a fraction of two integers.
Therefore, the rational numbers among the options are: b) -5 and c) 0.7 (recurring decimal).
Now, let's move on to some practice questions. I will provide you with a few questions, and you can try solving them. Afterwards, I will provide you with the answers.
Practice Questions:
1) Is -2 a rational number?
2) Write the decimal number 0.125 as a fraction.
3) Is √16 a rational number?
Take a few moments to solve these questions. Once you are ready or have finished solving them, let me know, and I will provide you with the answers.
Introduction to Rational Numbers Quick Check:
1) True or False: Irrational numbers can be expressed as a fraction of two integers.
Answer: False. Irrational numbers cannot be expressed as a fraction of two integers, whereas rational numbers can.
2) Which of the following numbers is rational?
a) √3
b) 0.25
c) π
d) -5.8
Answer: b) 0.25
3) Which of the following numbers is irrational?
a) 2/3
b) -1.5
c) √16
d) 7/8
Answer: c) √16
4) True or False: Every integer is also a rational number.
Answer: True. Every integer can be expressed as a fraction with a denominator of 1, making it a rational number.
5) Write the rational number that is equivalent to 0.6 as a fraction.
Answer: 0.6 can be written as 6/10, which can be further simplified to 3/5.
Practice:
1) Write the following irrational numbers as decimals:
a) √2
b) √10
c) √7
d) √13
2) Determine whether the following numbers are rational or irrational:
a) -2.7
b) 0.333...
c) 1.41421356
d) -5/7
3) Write the fraction equivalent of the following decimals:
a) 0.125
b) 0.6
c) 0.8
d) 0.333...
Answers:
Quick Check:
1) False
2) b) 0.25
3) c) √16
4) True
5) 3/5
Practice:
1)
a) approximately 1.414
b) approximately 3.162
c) approximately 2.646
d) approximately 3.605
2)
a) Rational
b) Rational (repeating decimal, can be expressed as 1/3)
c) Irrational (approximation of square root of 2)
d) Rational
3)
a) 1/8
b) 3/5
c) 4/5
d) 1/3